#REGRESSION ANALYSIS R STUDIO FOR FREE#
Try for free Linear Regression in R | A Step-by-Step Guide & Examples We add an asterisk here to indicate that the \(R^2\) in meta-regression is slightly different to the one used in conventional regressions, because we deal with true effect sizes instead of observed data points.Eliminate grammar errors and improve your writing with our free AI-powered grammar checker. \hat\theta_k = \theta + \beta x_\), can also be calculated for meta-regression. The formula for a meta-regression looks similar to the one of a normal regression model:
In meta-regression, the variable \(y\) we want to predict is the observed effect size \(\hat\theta_k\) of study \(k\). A standard regression equation, therefore, looks like this: In a conventional regression, we want to estimate the value \(y_i\) of person \(i\) using a predictor (or covariate) \(x_i\) with a regression coefficient \(\beta\). 20) mention that this guideline may also be applied to meta-regression models, but that it should not be seen as an iron-clad rule. In Chapter 7.2, we already covered that subgroup analyses often make no sense when \(K<\) 10. It also means that, while we conduct analyses on samples much larger than usual for primary studies, it is still possible that we do not have enough data points for a meta-regression to be useful. This is why we have to perform meta-regression with predictors on a study level. In meta-analyses, the individual data of each participant is usually not available, and we can only resort to aggregated results. In the past, you may have already performed a regression using primary study data, where participants are the unit of analysis. In the second part of this chapter, we will therefore also have a look at multiple meta-regression, and how we can conduct one using R. It is also very versatile: multiple meta-regression, for example, allows us to include not only one, but several predictor variables, along with their interaction. Meta-regression, although it has its own limitations, can be a very powerful tool in meta-analyses. In this chapter, we will delve a little deeper, and discuss why subgroup analysis and meta-regression are inherently related. We already mentioned in the last chapter that subgroup analysis is also based on a mixed-effects model. More importantly, however, it also uses one or more variables \(x\) to predict differences in the true effect sizes. This model accounts for the fact that observed studies deviate from the true overall effect due to sampling error and between-study heterogeneity. Meta-regression achieves this by assuming a mixed-effects model. In meta-regression, we also have to make sure that the model pays more attention to studies with a lower sampling error, since we can assume that their estimates are closer to the “truth”. In “normal” meta-analyses, we take this into account by giving studies a smaller or higher weight. In Chapter 3.1, we already learned that observed effect sizes \(\hat\theta\) can be more or less precise estimators of the study’s true effect, depending on their standard error. The fact that effect sizes are used as predicted variables, however, adds some complexity. Based on this information, a meta-regression model tries to predict \(y\), the study’s effect size. The variable \(x\) represents characteristics of studies, for example the year in which it was conducted. In meta-regression, this logic is applied to entire studies. Usually, regression models are based on data comprising individual persons or specimens, for which both the value of \(x\) and \(y\) is measured. In its simplest form, a regression model tries to use the value of some variable \(x\) to predict the value of another variable \(y\). Regression analysis is one of the most common statistical methods and used in various disciplines. It is very likely that you have heard the term “regression” before. We also mentioned that subgroup analyses are a special form of meta-regression. Instead, they allow us to investigate patterns of heterogeneity in our data, and what causes them. As we learned, subgroup analyses shift the focus of our analyses away from finding one overall effect.
N the last chapter, we added subgroup analyses as a new method to our meta-analytic “toolbox”.
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